Methods and devices for microelectromechanical resonators

ABSTRACT

MEMS based sensors, particularly capacitive sensors, potentially can address critical considerations for users including accuracy, repeatability, long-term stability, ease of calibration, resistance to chemical and physical contaminants, size, packaging, and cost effectiveness. Accordingly, it would be beneficial to exploit MEMS processes that allow for manufacturability and integration of resonator elements into cavities within the MEMS sensor that are at low pressure allowing high quality factor resonators and absolute pressure sensors to be implemented. Embodiments of the invention provide capacitive sensors and MEMS elements that can be implemented directly above silicon CMOS electronics.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/369,757, now U.S. Pat. No. 11,479,460, filed Mar. 29, 2019, which isa continuation of U.S. application Ser. No. 14/790,220, now U.S. Pat.No. 10,291,200, filed Jul. 2, 2015, which claims priority to U.S.Provisional Application No. 62/020,049, filed Jul. 2, 2014. Theforegoing applications are incorporated herein by reference in theirentireties.

FIELD OF THE INVENTION

The present invention relates to MEMS sensors and more particularly toMEMS resonators which may be manufactured directly over or inconjunction with silicon based CMOS electronics.

BACKGROUND OF THE INVENTION

Microelectromechanical systems (MEMS) are small integrated devices orsystems that combine electrical and mechanical components. Thecomponents can range in size from the sub-micrometer level to themillimeter level, and there can be any number, from one, to few, topotentially thousands or millions, in a particular system. HistoricallyMEMS devices have leveraged and extended the fabrication techniquesdeveloped for the silicon integrated circuit industry, namelylithography, doping, deposition, etching, etc. to add mechanicalelements such as beams, gears, diaphragms, and springs to siliconcircuits either as discrete devices or in combination with integratedsilicon electronics. Whilst the majority of development work has focusedon silicon (Si) electronics additional benefits may be derived fromintegrating MEMS devices onto other existing electronics platforms suchas silicon germanium (SiGe), gallium arsenide (GaAs) and, indiumphosphide (InP) for RF circuits and future potential electronicsplatforms such as organic based electronics, nanocrystals, etc.

Within the field of radio frequency integrated circuits (RFIC) highquality filters, resonators, oscillators are required and typically mustbe implemented as bulky off-chip surface-acoustic wave (SAW) filters toachieve a satisfactory quality factor (Q-factor). Whilst currentadvances in MEMS technology have made it possible to implement suchelements on-chip with a comparable Q-factor this is only achieved withinthe prior art through exploiting proper packaging techniques. Generally,these increase complexity, increase costs, and reduce yields asmechanical/physical sealing of the fabricated MEMS/MEMS-CMOS circuit isrequired. This is because the Q-factor of a MEMS resonating device isstrongly dependent on the level of vacuum in its environment as reducingpressure minimizes air resistance, resulting in reduced damping of themechanical structure's vibration.

However, the resonating elements of the MEMS are anchored to thesubstrate which yields anchor damping losses arising from the transferof kinetic energy from the resonator to its support structure.Mechanical vibrations within a MEMS travel as acoustic or elastic waveswhich when they impinge upon an interface, such as the resonator—anchorinterface then these waves may either be reflected or couple through theinterface to the substrate. Those elastic waves that couple to thesubstrate are lost and hence are an energy loss mechanism for theresonator. Anchor damping can impose considerable losses in MEMSresonators and thus dramatically affect the quality factor. Accordingly,it would be beneficial to reduce anchor damping losses in order toimprove the Q factor of resonating MEMS elements.

MEMS resonators are mechanical structures which in order to operaterequire an electrical input. Their output is a mechanical vibrationwhich is converted into an electrical signal in order to be “sensed” andsubsequently utilized. There are several transduction mechanisms thatconvert mechanical energy into electrical energy and in many instancesthe choice of the transduction mechanism is an important deciding factorin the MEMS resonator design. Electrostatic and piezoelectrictransduction mechanisms are most commonly used due to the ease offabrication and excellent performance of the designs. However,alternative methods based on optical and magneto-motive transduction doexist, and have met success.

Within the prior art relating to electrostatic transduction significantfocus has been made in respect of surface micromachining and reducingthe gaps between the actuating electrodes and the sensing electrodes.This focus being due to the fact that the electrostatic couplingcoefficient is inversely proportional to the square of the gap.Accordingly, over the past decade many implementations that required DCbiases of 150-200V, which is impractical for commercial consumerelectronics, have become commercially viable as research on surfacemicromachining led to gap reduction to dimensions significantly smallerthan 1p m, in some instances down to 30 nm. However, in this designprocess the electrostatic transduction area has been also limited by thethickness of the material, especially where the resonator is laterallydriven, that can be processed at these small dimensions). This beingaddition to reduced fabrication yields and in many instances use offabrication processes that were not amendable to mass-production.

Accordingly, it would be beneficial to establish resonators exploiting acombination of bulk and surface micromachining processes so that whilstthe gaps are increased to facilitate manufacturing with high yield theincreased thickness of the resonating elements results in thetransduction area being significantly increased allowing bias voltagesto be reduced to voltages compatible with high volume low cost consumerelectronics.

However, in essentially all applications, the important considerationsfor selecting a MEMS sensor include:

-   -   Accuracy;    -   Repeatability;    -   Long-term stability;    -   Ease of calibration;    -   Size;    -   Packaging; and    -   Cost effectiveness.

MEMS sensors require electronic circuits to either provide excitationand/or bias signals, as in the instance of MEMS resonators, or toconvert the MEMS sensor output to a signal for use by other electronics.Silicon CMOS electronics has become the predominant technology in analogand digital integrated circuits. This is essentially because of theunparalleled benefits available from CMOS in the areas of circuit size,operating speed, energy efficiency and manufacturing costs whichcontinue to improve from the geometric downsizing that comes with everynew generation of semiconductor manufacturing processes. In respect ofMEMS systems, CMOS is particularly suited as digital and analog circuitscan be designed in CMOS technologies with very low power consumption.This is due, on the digital side, to the fact that CMOS digital gatesdissipate power predominantly during operation and have very low staticpower consumption. This power consumption arising from the charging anddischarging of various load capacitances within the CMOS gates, mostlygate and wire capacitance, but also transistor drain and transistorsource capacitances, whenever they are switched. On the analog side,CMOS processes also offers power savings by offering viable operationwith sub-1V power supplies and with μA-scale bias currents.

Accordingly, it would be beneficial whilst designing MEMS resonators andabsolute pressure sensors it would be beneficial to establish theirdesigns such that they are compatible with combining the CMOS and MEMStechnologies into a single integrated circuit. It would be furtherbeneficial for the processes of manufacturing MEMS resonators andabsolute pressure sensors to support the integration of other capacitivesensors for other measurands within a single die and for the MEMSelements to be implemented directly atop silicon CMOS electronics (i.e.above integrated circuits, or above-IC) thereby minimizing footprint,cost, and parasitics.

Other aspects and features of the present invention will become apparentto those ordinarily skilled in the art upon review of the followingdescription of specific embodiments of the invention in conjunction withthe accompanying figures.

SUMMARY OF THE INVENTION

It is an object of the present invention to mitigate limitations withinthe prior art relating to MEMS sensors and more particularly to MEMSresonators which may be manufactured directly over or in conjunctionwith silicon based CMOS electronics.

In accordance with an embodiment of the invention there is provided aMEMS device comprising a membrane formed within a device layer, an uppercavity formed within a top layer, and a lower cavity formed within ahandling layer.

In accordance with an embodiment of the invention there is provided amethod comprising forming a lower cavity within a handling layer,bonding a device layer to the handling layer, processing the assembleddevice and handling layers in order to form a membrane within the devicelayer which is released from the device and handling layers, forming anupper cavity within a top layer, and bonding the top layer to theassembled device and handling layers within a predetermined pressureenvironment in order to seal the membrane within a cavity formed by theupper cavity and the lower cavity.

In accordance with an embodiment of the invention there is provided aMEMS device comprising a disk resonator and a plurality of ringresonators deployed around the periphery of the disk resonator, whereineach ring resonator is coupled to the disk resonator by a short beam andthe disk resonator acts as the anchor for each ring resonator of theplurality of ring resonators.

In accordance with an embodiment of the invention there is provided aMEMS device comprising:

-   -   a first electrode having a first edge;    -   a second moveable electrode having a second edge disposed        opposite the first edge and an inner open region;    -   a stop disposed within the inner open region of the second        electrode positioned to stop the second edge of the second        moveable electrode at a predetermined separation from the first        edge of the first electrode when the second moveable electrode        is pulled towards the first electrode under electrostatic        actuation; and    -   at least one welding pad of a plurality of welding pads disposed        on a second edge of the second moveable electrode on the inner        open region engaging against the stop, wherein the at least one        welding pad of a plurality of welding pads is dimensioned to        short the second electrode to the stop and melt fusing the        second electrode to the stop during the pulling in such that the        resulting electrode gap between the first edge and the second        edge is smaller than the minimum resolvable gap of the MEMS        fabrication process employed to form the electrodes as part of        the MEMS device.

Other aspects and features of the present invention will become apparentto those ordinarily skilled in the art upon review of the followingdescription of specific embodiments of the invention in conjunction withthe accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way ofexample only, with reference to the attached Figures, wherein:

FIG. 1 depicts a simple model for an electrostatically driven MEMSresonator;

FIG. 2 depicts the effect of pressure upon MEMS resonators;

FIG. 3 depicts a differential measurement setup for a Lame moderesonator;

FIG. 4 depicts a differential measurement setup for a Lame moderesonator according to an embodiment of the invention;

FIG. 5 depicts a free-free beam resonator according to an embodiment ofthe invention;

FIG. 6 depicts a 2-ring breathing-mode resonator according to anembodiment of the invention;

FIGS. 7A and 7B depict schematics of a 4-ring breathing-mode resonatorusing resonant disk anchors according to an embodiment of the invention;

FIG. 8 depicts the frequency response of 4-ring disk-coupled resonatoraccording to an embodiment of the invention showing peaks correspondingto the resonant frequencies of the disk and rings respectively;

FIG. 9 depicts a double ended tuning fork resonator according to anembodiment of the invention;

FIG. 10 depicts a movable electrode configuration according to anembodiment of the invention;

FIG. 11 depicts the movable electrode configuration depicted in FIG. 10applied to a square Lame mode resonator according to an embodiment ofthe invention;

FIG. 12 depicts the wine-glass mode of a disk resonator and Lame mode ofa square resonator with resonators anchored at the central nodal pointaccording to embodiments of the invention;

FIGS. 13 and 14 depict schematics of centrally anchored Lame mode anddisk resonators according to embodiments of the invention;

FIGS. 15 and 16 depict cross sectional schematic and SEM images of Lameresonators according to embodiments of the invention and packagedencapsulated die as manufactured upon a commercial MEMS fabricationprocess line;

FIG. 17 depicts the electrical characteristics of a square Lameresonator with corner anchors according to an embodiment of theinvention;

FIG. 18 depicts the electrostatic softening of the resonant frequencyfor a square Lame mode resonator according to an embodiment of theinvention;

FIG. 19 depicts the variation of motional resistance and resonantfrequency with bias voltage for a square Lame mode resonator accordingto an embodiment of the invention;

FIGS. 20A to 20E depict a process flow for fabricating MEMS resonatorsaccording to embodiments of the invention exploiting a commercial MEMSfabrication process line; and

FIG. 20F depicts an exploded perspective view of a MEMS resonatorsaccording to embodiments of the invention exploiting a commercial MEMSfabrication process line; and

FIG. 21 depicts flip-chip bonding of a MEMS resonator according toembodiments of the invention exploiting a commercial MEMS fabricationprocess line.

DETAILED DESCRIPTION

The present invention is directed to MEMS sensors and more particularlyto MEMS resonators which may be manufactured directly over or inconjunction with silicon based CMOS electronics.

The ensuing description provides exemplary embodiment(s) only, and isnot intended to limit the scope, applicability or configuration of thedisclosure. Rather, the ensuing description of the exemplaryembodiment(s) will provide those skilled in the art with an enablingdescription for implementing an exemplary embodiment. It beingunderstood that various changes may be made in the function andarrangement of elements without departing from the spirit and scope asset forth in the appended claims.

Mems Resonator

Modern consumer electronic devices impose stringent requirements of lowcost, low assembly complexity, compact system integration, highfunctionality, and low power consumption. Accordingly, MEMS resonatorswhich offer reduced production costs through batch manufacturingleveraging silicon integrated circuit design and manufacturingmethodologies have been of significant interest due to the potential forremoving the requirement for separate crystal oscillator components.Over the past 50 years since their first demonstration in 1967significant research focus has been applied to MEMS resonators. However,MEMS after an initial wave of optimism had to wait for manufacturingadvances, commercial requirements, and technological breakthroughs torealize their potential with effective designs, stable performance, andefficient operation. Such technological breakthroughs include, but arenot limited to, anchor damping, gas damping, thermoelastic dissipation,thermal expansion and the thermal coefficient of elasticity.

In general a MEMS resonator may be represented mechanically as amass-spring-damper second order system wherein the spring and mass areused to describe the oscillation while the damper is used to describethe energy losses. The resonant frequency, ƒ₀, of such a system can befound from Equation (1) where, k represents the spring constant and mthe mass of the resonating structure. The damper within themass-spring-damper second order system according to its magnitude whilstreducing, restricting or preventing its oscillations defines the overallsystem as being overdamped, critically damped, underdamped, or undamped.Accordingly, from this simplified perspective view the frequency ofoperation can be controlled by changing the spring constant and/or massof the resonating structure.

$\begin{matrix}{f_{0} = {\frac{1}{2\pi}\sqrt{\frac{k}{m}}}} & (1)\end{matrix}$

As noted supra a resonator has an output which is a mechanical vibrationwhich is converted into an electrical signal in order for it to be“sensed” and subsequently utilized which is generated in dependence uponan electrical input signal. Whilst there are different transductionmechanisms that convert mechanical energy into electrical energyelectrostatic and piezoelectric transduction mechanisms are the mostcommonly used due to their relative ease of fabrication and performance.In general, MEMS resonators based on electrostatic transduction offeradvantages including high quality factor, low phase noise, low powerconsumption and very low space requirements. MEMS resonators that arebased on electrostatic transduction are usually composed of a semi-freemoving structure, an actuating electrode and a sensing electrode. Asimplified model of an electrostatically driven MEMS resonator isdepicted in FIG. 1 comprising a drive electrode 110, resonator 120, andsensing electrode 130. A sinusoidal signal at the drive electrode 110 isused to drive the resonator 120 into oscillation at its naturalfrequency of vibration. The mechanical displacement causes a change inthe capacitance of the space between the sensing electrode and theresonating structure. This variation of the capacitance causes an outputcurrent at the sensing electrode 130. The electrical signal that isproduced has the same frequency as the natural mechanical frequency ofthe vibrating structure.

The electrostatic coupling coefficient, η, which defines the efficiencyof the electrostatic transduction for a simple electrostatically drivenresonator such as that depicted in FIG. 1 , for example, is defined byEquation (2) where C is the capacitance between the resonating structureand the sensing electrode, V_(P) is the DC potential difference betweenthe bias electrode(s) and the resonating structure, A is the electrodeoverlap area, ε_(r) is the relative permittivity of the material betweenthe structures, and d is the transducer gap.

$\begin{matrix}{\eta = {{V_{p}\frac{\delta C}{\delta x}} = {\varepsilon_{r}\frac{V_{r}A}{d^{2}}}}} & (2)\end{matrix}$

A number of important points can be extracted from Equation (2). Thefirst to note is that η is inversely proportional to the square of thetransducer gap, d. Because of the exponential nature of thisrelationship then the transducer gap is typically designed to be assmall as possible within the limits of the microfabrication processemployed. Thus, a series of attempts have been made to reduce it toseveral tens to few hundreds of nanometer levels. The limitations ofetching and photolithography have led researchers to employ innovativefabrication methods. In particular, the most common technique involvesdepositing an exceptionally thin film of silicon dioxide between thestructures. The film is then etched away with dry or wet etching,leaving in place an approximately 100-200 nm gap, see for example Nabkiet al. in “A Highly Integrated 1.8 GHz Frequency Synthesizer Based on aMEMS Resonator” (IEEE J. Solid-State Circuits, Vol. 44, pp. 2154-2168).Another point to be noted from Equation (2) is that the electrostaticefficiency depends on the potential voltage, V_(P), across the structureproviding designers with a tool to control the operation of theresonator. Accordingly a 0V bias voltage will switch off the devicecompletely and reduce the power consumption to effectively 0 W which canbe extremely important in portable electronic devices where powerefficiency is of the outermost importance.

Setting V_(P) to a high bias voltage leads to an increase in theelectrostatic efficiency. However, there are a number of limitationsthat restrict the use of a high V_(P). First, most electronic devicesoperate at a voltage range of 1.8V to 15V, anything beyond that islargely overlooked by commercial manufacturers. Second, high biasvoltages cause the devices to exhibit high non-linearity, leading toincreased phase noise and a reduced quality factor.

A. Quality Factor and Energy Losses

Resonating systems can be defined to a large degree by two parameters,the resonant frequency, ƒ₀ and the quality factor, Q. The resonancefrequency is the frequency at which the device exhibits higheramplitudes of vibration compared to other frequencies. The qualityfactor is defined by Equation (3) which is a dimensionless parameterthat characterizes a resonator's operation from two perspectives. First,it provides information regarding its efficiency as a high Q indicatesthat the oscillations will die slowly and that there is little energylost during the periodic oscillation. Second, it provides informationregarding the relation of the resonator's bandwidth and center frequencyas Equation (3) may be rewritten as Equation (4) where Δƒ is thehalf-power bandwidth. A high Q is associated with very high selectivity,small Δƒ, which is very desirable in RF filters.

$\begin{matrix}{Q = {2\pi\frac{En{ergyStored}}{En{ergyDissipatedPerCycle}}}} & (3)\end{matrix}$ $\begin{matrix}{Q = \frac{f_{0}}{\Delta f}} & (4)\end{matrix}$

Importantly, the Q of a resonator is highly dependent on the frequencyof operation. In general, it is more difficult to achieve high-Q at veryhigh frequencies (VHF) as anchor damping, thermoelastic dissipation andmaterial non-linearities become increasingly harder to counter. As such,the Q-ƒ product is very commonly seen in the literature because itincorporates the frequency dependency and allows for a more “fair”comparison of the various resonator designs. As is the case for aphysical resonator, a MEMS resonator slowly loses energy to thesurrounding environment. The usual macroscopic energy loss mechanismssuch as air damping and anchor damping remain in MEMS devices. However,the micro dimensions and the small energies involved emphasize theimportance of energy loss mechanisms that were previously not important,such as, the thermoelastic dissipation and surface losses. The finalquality factor of a MEMS resonator device can be found by adding theindividual contributions of each factor according to Equation (5).

$\begin{matrix}{\frac{1}{Q_{total}} = {\frac{1}{Q_{anchor}} + \frac{1}{Q_{gas}} + \frac{1}{Q_{TED}} + \frac{1}{Q_{surface}}}} & (5)\end{matrix}$

A.1. Gas Damping: Gas damping describes the transfer of kinetic energyfrom the resonator to the surrounding air. In electrostatic transductionresonators air damping is the dominant energy loss mechanism afteranchor damping, when operated at near atmospheric level pressures.Typically, the small gap between the input-output electrodes and theresonator gap, as well as the high vibration speeds involved, introducessignificant Couette flow damping, see for example Kaul in“Microelectronics to Nanoelectronics: Materials, Devices &Manufacturability” (CRC Press). Further, with very narrow gaps at thesub-micron level, other more complicated mechanisms, such as squeezefilm damping, can cause further reductions in the Q of the resonators,see for example Kun. Because of this electrostatic MEMS resonators aregenerally operated in vacuum or very low pressure environments. Underthese conditions the remaining air behaves as kinetic particles ratherthan a continuous medium.

A.2. Anchor Damping: Anchor damping describes the transfer of kineticenergy from the resonator to its support structure. Mechanicalvibrations travel at the speed of sound within the medium of theresonator through waves known as elastic waves. When these waves meetthe resonator/anchor interface then these elastic waves may either getreflected or traverse through to the substrate. Elastic waves traversingto the substrate are lost as is the energy that they contain. As aresult, anchor damping can impose considerable losses in MEMS resonatorsand thus dramatically affect the quality factor. However, usingtechniques from other electromagnetic wave systems researchers haveexploited impedance matching techniques, such as quarter-wavelengthmatching, to reduce this loss mechanism.

B: Resonator Developments According to Embodiments of the Invention

According to embodiments of the invention the inventors address the lossmechanisms within MEMS based resonators, including:

B1. Air Damping Losses: Within the prior art MEMS resonators aretypically packaged within an external package under vacuum or lowpressure as part of an overall silicon circuit or an assembly such as asystem-in-package, system-on-a-chip, etc. Such packages, may include,but are not limited to, hermetic metal/glass using typically Kovar™ withglass-seal electrical feed throughs, and hermetic ceramic packages usingtypically lead frames embedded in a vitreous paste between ceramic topand bottom covers. In some prior art approaches encapsulation of theMEMS is performed through wafer-scale thin film encapsulationor throughvacuum micro-cavities formed through van der Waals bonding of siliconand/or borosilicate glass). As evident from FIG. 2 the quality factor ofa MEMS resonator is not limited by gas damping at pressures below 10 Pa,see for example Hopcroft in “Temperature-Stabilized Silicon Resonatorsfor Frequency References” (PhD Dissertation, Mechanical Engineering,Stanford University, 2007). Accordingly, it is desirable to fabricateMEMS resonators through a commercial MEMS process line that supportswafer level encapsulation such that large numbers of MEMS resonators canbe simultaneously packaged at very low pressures, i.e. ˜10 mTorr (˜1.5Pa), as achieved on the MEMS Integrated Design for Inertial Sensorscommercial MEMS process line of Teledyne DALSA Inc.

B2. Electrostatic Transduction—DC Bias: Within the prior art theresonators found in the literature concentrate on surface micromachiningand reducing the transduction gaps between the actuating electrodes andthe sensing electrodes. As evident from Equation (2) the electrostaticcoupling coefficient is inversely proportional to the square of the gapsuch that many implementations require DC biases of 150-200V, which isimpractical for commercial consumer electronics applications.Accordingly, the past decade therefore research has tended toconcentrate on exploiting surface micromachining techniques to furtherreduce the gaps to dimensions significantly below 1 μm. However, thesetechniques limit the electrostatic transduction area as the processconstraints for fabricating these narrow gaps leads to limits for thematerial thickness being etched. Such limitations are particularlyimportant especially if the resonator is laterally driven but have ledto low bias voltages through gaps as low as 30 nm. However, thesetechniques have led to low fabrication yields and are not amicable tomass-production.

According to embodiments of the invention the MEMS resonators aredifferentiated in the combination of bulk and surface micromachiningprocesses. The minimum gap is approximately 1.5 μm but the devices areapproximately 30 μm thick and laterally driven. Accordingly, thetransduction area A is massively increased with respect to prior artMEMS resonators allowing the bias voltage to be reduced to approximately5V whilst the larger electrode gaps lead to high manufacturing yields.

B.3. Anchor Losses: Embodiments of the invention exploited impedancematching techniques to address anchor losses.

B.4. Electronics Compatibility: Embodiments of the invention exploitmanufacturing techniques that are compatible with silicon CMOS.

B.5. Packaging: Embodiments of the invention exploit multi-layer deviceimplementation and packaging as described below allowing localizedencapsulation of the MEMS devices with high vacuum levels to be achievedyielding high Q levels to be achieved.

C. Resonator Device Designs

C.1. Resonant Frequency Tuning of Bulk Mode MEMS Resonator

Within prior art resonators a change in the DC bias introduces afrequency shift in the resonant frequency of the element, a phenomenonreferred to as electrostatic spring softening. A voltage differencebetween the electrodes and the resonating mass will introduce anelectrostatic force F_(E) according to Equation (6), where C is thecapacitance, V is the voltage and d is the distance between the twoparallel plates. This electrostatic force is applied on the resonantmass, pushing it or pulling away from the, generally, fixed driving andsensing electrodes. This effect induces a strain across the structure,which will affect the resonant frequency according to Equation (1). Achange in the applied voltage will change the applied force, which inturn will affect the resonant frequency of the device.

$\begin{matrix}{F_{E} = {\frac{1}{2}\frac{C}{d}V^{2}}} & (6)\end{matrix}$

This dependency has been exploited and is currently used to provideprogrammable resonators (oscillators) wherein the resonant frequency iselectrically tuned through the DC bias. However, a drawback with thisapproach is that the output current of the resonator is also depended onthe DC bias voltage. When the DC bias is changed, the overall frequencyresponse of the device is affected not just the resonant frequency, andthis introduces two challenges. First, when the DC bias is reduced themotional resistance is exponentially increased. In order for the deviceto continue operating as an oscillator, the amplifier's gain in thenegative feedback loop needs to be increased accordingly. Second, whenthe DC bias is increased past a certain threshold, the resonator beginsoperating in an unpredictable non-linear regime.

The method inventive described below can be used to set, tune or adjustthe output frequency of a MEMS resonator without affecting the outputcurrent. Whilst the discussion that follows, refers to a square Lamemode resonator the method may be applied to essentially any suitableresonating element provided that it has sufficient actuation space onthe top or bottom surface. The device consists of the classic squareLame mode resonator that is sensed and actuated using a fullydifferential setup such as that depicted in FIG. 3 . As depicted thesquare Lame mode resonator has a pair of drive electrodes denoted byD+/D− and a pair of sense electrodes S+/S− disposed around its peripherywhilst the resonator body itself is DC biased through a contact at ananchoring point, in this instance the corners.

A square resonator mass is anchored in 4 corners using Finite ElementMethod (FEM) optimized anchors. Two electrodes are used to provide twodrive signals that are 1800 out of phase to the D+/D− electrodes.Another set of electrodes, S+/S−, are used to collect the two out ofphase output signals and recombine them. The bias voltage is provided tothe resonating mass using a fifth electrode. Typically this would beused for frequency tuning; for the purposes of this specification thiswill be referred to as the legacy configuration or model.

The inventors novel methodology is based upon the introduction ofadditional electrodes on the top or bottom side of the resonator thatare independent of the DC bias, as illustrated in FIG. 4 with contacts420 disposed in the corners of the square resonator disk 410 andindependent from the drive electrodes 430, sense electrodes 440 and biaselectrode 450. Different configurations with different electrodearrangements may be implemented without departing from the scope of theinvention.

The inventors have identified advantages of the inventive designmethodology including, firstly, that the use of several tuningelectrodes allows for the introduction of complex strains on theresonant structure that were previously unachievable. For the purposesof this specification, complex strains refers to strains that are notuniform in direction but rather spread in different directions andinterfere constructively or destructively across the structure. Asdiscussed previously the prior model of frequency tuning yields adependency on the DC bias which is linear. In contrast, embodiments ofthe invention, with complex strain, implemented by using sets ofdifferent electrodes can introduce exponential or polynomial dependencyof resonator frequency with DC tuning voltages applied. Additionally,each tuning electrode is independent and its voltage can be setseparately, effectively allowing for high tuning resolution.

Amongst the applications for such inventive tuning methodology istemperature compensation. This is because the resonant frequency ofsilicon resonators decreases according to a quadratic formula as thetemperature increases. Accordingly, a multiple electrode configurationmay be established that yields a tuning configuration that couldcompletely or significantly null the resonant frequency temperaturedependence. Hence, a linear sensing of the temperature may yield alinear DC bias variation with temperature that generates a quadraticfrequency offset to compensate for the temperature dependent frequencyoffset.

A second advantage for such inventive tuning methodology is that thefrequency tuning range dramatically increases compared to the prior artconfiguration. This is because there is effectively no upper or lowerlimit imposed by non-linearity and the motional impedance of the device.The tuning voltage can be positive, negative or zero depending on thetuning configuration that needs to be implemented.

Due to the methodology of the commercial MEMS process line described anddepicted in FIGS. 20A-20F metallization of the thick silicon MEMSstructures on either side is a relatively straight forward processingaddition. However, it would be evident that in other MEMS manufacturingsequences the provisioning of additional electrodes underneath MEMSstructural elements with wrap-around metallization etc. and on the uppersurface may be implemented. Whilst upper surface metallization of a MEMSstructural element may be considered a standard processing step as upperwafer metallization is required and implemented for electricalinterconnect etc. techniques exist within the prior art such as reportedby Nabki et al. in “Low-stress CMOS-compatible silicon carbidesurface-micromachining technology-Part I: Process development andcharacterization” (J. Microelectromechanical Sys., Vol. 20.3, pp.720-729), “Low-stress CMOS-compatible silicon carbidesurface-micromachining technology-Part II: Beam resonators for MEMSabove IC” (J. Microelectromechanical Systems, Vol. 20.3, pp. 730-744)and World Intellectual Property Office publication WO/2010/003,228 “LowTemperature Ceramic Microelectromechanical Structures”.

C.2. Free-Free Beam Resonator

A free-free beam resonator comprises a main resonating structure, knownas the Free-Free beam, and four supporting torsional beams placed at theflexural nodal points of the structure. The supports are suspended overthe ground plate and subsequently connected to rigid contact anchors. Anelectrode next to the Free-Free beam is responsible for providing therequired electrostatic excitation via an applied AC voltage (V_(AC)). Asensing electrode is located on the opposite side of the beam in orderto “sense” the capacitive change. A DC bias voltage (VDC) applied on theresonating structure is responsible for amplifying the weakelectrostatic force that is created by V_(AC). Such a free-free beamresonator according to an embodiment of the invention is depicted inFIG. 5 as a perspective schematic and with detail of the resonatorshowing the 30 μm thick MEMS beam and torsion mounts. Accordingly, thebeam may support electrodes for the inventive tuning methodology.

C.3. 2-Ring Breathing Mode MEMS Resonator

A 2-ring breathing mode MEMS resonator consists of two ring resonatorsthat operate in the so-called breathing mode of vibration, namelyexpansion—contraction. Through a fully differential drive/sensingconfiguration, as depicted in FIG. 6 , cancellation of any feed-throughand allows for reduction of the required DC bias. A mechanical beam isused to connect and couple the two breathing mode resonators where thebeam is designed so that its extensional mode of vibration matches theextensional mode of the ring resonators. With appropriate design theresulting resonator is limited in Q by only the Akheiser limit andThermo Elastic Dissipation (TED).

Referring to Table 1 there is presented performance of a 2-ringbreathing mode resonator according to an embodiment of the inventionexploiting 30 μm deep structures with gaps suited to high volumemanufacturing on a wide range of commercial foundry processes.

TABLE 1 2-Ring Breathing Mode MEMS Resonator Performance ParameterPerformance Resonant Frequency (MHz) 10 Quality Factor (Q) ~400,000Polarization Voltage (V) 5 Gap (μm) 1.5 Vacuum Encapsulation Yes VacuumLevel 1.5 Pa Q at Atmospheric Pressure ~400,000

C.4. 4-Ring Breathing Mode MEMS Resonator using Disc Resonator Anchor

The inventors have established a MEMS resonator design employing ringresonators in combination with a central disk resonator which act as theanchor to the ring resonators. Accordingly, the MEMS resonator operatesin the breathing mode and radial modes respectively. The disk resonatoracts as the anchor of the device. Impedance matching is achieved bymatching the resonant frequency of the central disk resonator and thering resonators. Theoretically this is accomplished by matchingequations (7) and (8) for the ring and disc respectively, where, E isthe Young's modulus of elasticity, ρ is the density, ν is Poisson'sratio, R₁, R₂ are the inner and outer radius of the ring resonator and Ris the radius of the disk resonator. The structures are connected byshort straight beams 740 as can be seen in FIGS. 7A and 7B which depictplan and perspective views of a 4-ring breathing mode MEMS resonatorwith a disc resonator anchor according to an embodiment of theinvention. As depicted four ring resonators 740 each comprisingdisc/driving electrode 720 and sensing electrode 730 4.4 which aredisposed around the periphery of the central disk resonator 710. Thedevice can be operated using a fully differential configuration thatcancels out the effects of the feedthrough capacitance. There are fouractuation electrodes and 4 sensing electrodes. The DC bias is applied tothe disk resonator through its central anchor.

$\begin{matrix}{f_{RING} = {\frac{1}{2\pi}\sqrt{\frac{E}{\rho R_{1}R_{2}}}}} & (7)\end{matrix}$ $\begin{matrix}{f_{DISC} = {\frac{k_{M}}{2\pi R}\sqrt{\frac{E}{\rho( {1 - \nu^{2}} )}}}} & (8)\end{matrix}$

This novel configuration has several advantages the prior art. Firstly,the impedance matching that can be achieved between the disk and ringresonators is of higher quality than what can be achieved between ringsand beam structures. Effectively this leads to a higher f-Q product,which is an important issue in the operation of a resonator as anoscillator. The second advantage is that the use of four rings insteadof two leads to a drastic drop in the motional resistance of the device.This is because the electrostatic transduction area is effectivelydoubled but without impacting the stiffness of the anchors. Thirdly, thedisk-ring coupling allows for the introduction of additional ringresonators without significant changes to the design. The proposeddesign with four rings can be easily modified to include an additionalfour rings, leading to ultra-low power devices, with eight ringresonators. Whilst the design depicted in FIGS. 7A and 7B is a circulardisk it would be evident that disk resonator designs such as square,octagonal, etc. may exploit the advantages of the ring resonators asanchors.

Beneficially, a design variation of the disk resonator in combinationwith ring resonators can be used in order to create filter devices.Accordingly, a resonant frequency shift between the ring resonators andthe disk resonator is introduced. FIG. 8 depicts such an instance withthe frequency response wherein the four ring resonators have a slightresonant frequency offset compared to the disk resonator. Filters withdifferent band-pass frequencies and band-pass frequency characteristicsmay be implemented by changing the dimensions of the ring resonators. Itshould be noted that the dimensions of each ring can be tunedindependently in order to achieve the desired filter response. Furthermore complex combinations can be considered such that the disk resonatoris offset from the ring resonators which are themselves offset asopposing pairs for example from the other opposing pairs of ringresonators.

It would be evident that the area of the disk resonator allows for theimplementation of the inventive concept of additional control electrodesas described and discussed supra in respect of additional electrodes onthe top or bottom side of the resonator that are independent of the DCbias (see Section A3.A).

C.5. Double Ended Tuning Fork Resonator: Double Ended Tuning Fork (DETF)resonators as depicted in FIG. 9 consist of two clamped-clamped beamswherein the masses at the front and back of the beams couple themtogether so that they resonate at the same frequency. A bias voltage maybe applied to the resonating structure whilst two drive electrodes areused in order to actuate each clamped-clamped beam. The capacitancechange is measured from a center “sense” electrode. Based upon thecommercial MEMS process line the inventors have established DEFT designswith large transduction gaps (≈1 μM) such that at 1 MHz a MEMS resonatoraccording to an embodiment of the invention may operate with DC biasvoltages in the range of 10-15V, while the quality factor isapproximately 10,000. A DEFT may also allow for the implementation ofthe inventive concept of additional control electrodes as described anddiscussed supra in respect of additional electrodes on the top or bottomside of the resonator that are independent of the DC bias (see SectionA3.A).

C.6. Post-Fabrication Gap Reduction

Within the prior art resonator structures are design, fabricated, andtested. The devices are calibrated and/or electrically tuned and ifnecessary their associated control/drive/sense electronics similarlyelectrically tuned or provided with the calibration data in order tocompensate for variations in the manufacturing process. However, theinventors have established a design methodology that allows forpost-fabrication reduction of the transduction gap in capacitiveelectrostatic devices. Accordingly, devices can be manufactured withlarger electrode gaps, increasing yields and lower processingcomplexity, where the gaps are subsequently reduced for operation of thedevice.

The inventive method lies in the combination of two elements. First, theelectrode configuration that is used is movable instead of fixed whichis accomplished by anchoring the electrodes using a serpentinestructure. The electrode structure can have a rectangular, elliptical orcircular shape but it the embodiments described below it is open or“hollow”. The second key element of the design is the inclusion of astop or island anchor which, when the electrode structure is“hollow”/open, is inside the movable electrode. The overallconfiguration can be seen in FIG. 10 . The initial electrode-stop gap isestablished at 1.5 μM, although the desired operating regime for theMEMS devices is with a 0.05 μm gap. The initial electrode-resonator gapmay be set at or above the minimum process value, which for example maybe anything above 1.5 μM, for the purposes of this work it was set to1.55 μm. Accordingly, a voltage differential between the drive and/orsense electrode and the resonating mass pulls the electrode towards theresonating mass. After the electrode has moved the required distance,e.g. 1.5 μm, then it hits a “stop” structure. At this point theresulting electrode-resonator gap will be 0.05 μm. It would be evidentthat alternatively the electrode gap may be 1.75 μm and the stop set1.70 μm away such that again the final resulting electrode-resonator gapwill be 0.05 μm although the driving voltage to close the gap will belarger. Similarly the difference may be set to other values to establishother final gaps. It would be evident that design flexibility existsaccording to final target gap, process line constraints, etc.

Referring to FIG. 10 there is depicted a perspective view 1000A of theinventive concept employing an open or “hollow” electrode A 1040 thathas an edge disposed parallel to electrode B 1010. Within the electrodeA 1040 is stop 1020, while additionally, electrode A 1040 has a firstgap (G1=1.55 μm) on the upper side towards electrode B 1010, and asecond gap (G2=1.55 μm) on the lower side. Accordingly applying avoltage to electrode A 1040 results in pull-in of the electrode towardselectrode B 1010 until the electrode A 1040 hits the stop 1020 such thatthe resulting gap between electrode A 1040 and electrode B 1010 is nowG1−G2=1.55−1.50=0.05 μm.

Now if a current is passed through the electrode-stop contact (electrodeA 1040—stop 1020) it will heat the area and if the current is increasedsufficiently the silicon will melt and the two structures will be weldedtogether. Within the prior art the welding of silicon has been reportedbut with prior art electrode configurations significant variation in thewelding results was obtained which rendered the solution commerciallyunsuitable. The inventors surmise that the most likely reason for thiswas that the contact area was too large with wide asperity variability.The result is that there is a large probability that the contactresistance will be either too high or too low. Accordingly, theinventors have designed a variation to the electrodes which they referto as “welding pads” 1030 as depicted in the expanded view of the regionbetween stop 1020 and electrode A 1040. These are small structures thatprotrude from the face of the electrode or the stop structure. When theelectrode pulls in to the “stop” structure, the welding pad will be theonly contact area. A current passing through the electrode-stop contactwill only melt the welding pad. While the contact resistance is likelyto increase, the repeatability and reliability of the welding willincrease. For example, a configuration of the welding pad on each sideof the structure may be 5 μm×0.5 μm (W×L) such that the majority of theelectrode—stop are separated by the welding pad 1030 length, e.g. L=0.50μm. It would be evident that it would be possible to increase ordecrease the number or dimensions of the welding pads depending ondesirable contact resistance.

It would also be evident that whilst the configuration of an openelectrode with stop disposed within is conceptually and topographicallyneat that other embodiments may be implemented without departing fromthe scope of the invention. In essence all that is required is a portionof the electrode and a stop are disposed at a predetermined spacing,such that pull-in of the electrode results in the electrode contactingthe stop such that the electrode is now disposed at the desiredseparation from another electrode or feature of the MEMS device, andthat the structure allows electrical current flow to weld the stop andelectrode together. As noted the employment of small “welding pads”provides welding controllability to allow the method to operate within acommercial MEMS production environment. As the separation ismechanically limited it would be evident that the electrode pull-in andwelding process may be automatically performed on MEMS devices employingembodiments of the invention.

Referring to FIG. 11 there are depicted perspective 1100A and plan 1100Bviews of the electrode gap reduction method according to an embodimentof the invention applied to the design and manufacture of a square Lamemode resonator. However, it would be evident that the design methodologycan be used on any capacitive electrostatic device. With the square Lamemode resonator the movable electrode structure was replicated on each ofthe four sides of the resonator. Analysis by the inventors indicatesthat the motional impedance of the device is expected to drop by morethan 90%.

C.7. Centrally Anchored Bulk Mode Resonators

Within the description supra resonators have been primarily describedand depicted with edge/corner anchors. However, resonators may be formedusing a central anchor such as depicted in first image 1200A in FIG. 12which depicts a so-called “wine-glass mode” of vibration for a circulardisk resonator, whilst second image 1200B in FIG. 12 depicts the Lamemode of vibration for a square resonator. Both modes can be seen to have5 quasi-nodal points, four located in the perimeter of the resonantelement and one in the center. Within the prior art bulk mode resonatorshave been anchored using the quasi-nodal points located at theperimeter. However, a significant issue for such approaches is that asthe size of the resonator increases then there is a significant increasein the complexity required for the design and fabrication of theanchors. Further, such anchors make it effectively impossible to coupletwo consecutive bulk mode resonators in order to create a filter.

An essential factor in the prior art solutions maintaining perimeteranchors has been that the commonly available microfabrication processesdo not allow for the fabrication of designs anchored using the centernodal point whilst at the same time providing an electrically conductivepath. However, the inventors have overcome these limitations through theexploitation of a multi-wafer MEMS fabrication process comprising threewafers. These being:

-   -   a first (bottom) wafer which is etched in order to create a deep        cavity (e.g. 30 μm deep) together with a small island which is        strategically not etched in the center and will be subsequently        used to anchor the resonating element;    -   a second wafer, for example 30 μm thick, is then fusion-bonded        with the first wafer and processed using deep reactive ion        etching (DRIE) in order to define the resonator structure; and    -   a third wafer is patterned with Through Silicon Via (TSV) which        are to provide electrically conductive paths to the vacuum        encapsulated device when the third wafer is fusion bonded to the        second wafer in a vacuum environment which has a cavity also        etched into it (e.g. 20 μm deep) together with another small        island which is strategically not etched in the center and will        be subsequently used to anchor the resonating element.

A TSV is strategically placed so that it aligns with the center of thebulk mode resonator. Implementations for both a square and a disk bulkmode resonator are shown in FIGS. 13 and 14 respectively which have beenfabricated and fully characterized. The resulting cross-section fromsuch an assembly is depicted in FIG. 15 wherein the resonator is evidentin the center mounted to the lower “island” formed within the firstwafer and “pinned” by the subsequent attachment of the third wafer andit's “island” after the resonator has been DRIE'd to separate it fromthe second wafer. An exemplary manufacturing process is described belowin respect of Section D. The results obtained for square and circularsummarized in Table 2 below. These results show that the performance ofthe proposed devices is equivalent to on par with current state of theart devices. Such centrally anchored resonators have significantbenefits including the ability to couple multiple resonator devicestogether in order to create a filter or in order to lower the motionalimpedance of a composite resonator. Additionally, a reduction in thecentral anchor diameter would be anticipated to increase the qualityfactor of the devices.

TABLE 2 Experimental Results for Disk and Square Resonators with CentralAnchor Central Anchor - Central Anchor - Disk Square Resonant Frequency(MHz) 8.75 6.91 Quality Factor (Q) 823,000 779,000 Polarization Voltage(V) 20 V 50 V Transduction Gap (μm) 1.5 1.5 Vacuum Encapsulation Yes YesVacuum Level 1.5 Pa 1.5 Pa

C.8. Corner Anchored Square Lamé Mode Resonator

A square Lame mode resonator with dimensions 600 μm×600 μm×30 μm wasfabricated using an exemplary fabrication process described in Section Don <100> orientated silicon. The design, shown schematically in FIG. 3 ,employs four straight anchors, 60 μm×10 μm×30 μm to support theresonator. The inventors deemed that T-shape anchors were not necessaryas the resonator is not operated in the square-extensional mode. Thetransduction gap was designed to be 1.5 μm to meet the minimum gap sizeallowed by the fabrication process adopted. As noted supra whilst thisgap is large for electrostatically actuated resonator, but the thickness(30 μm) of the device allows the polarization voltage to be kept down toaround 40V. Referring to FIG. 16 there are depicted first to thirdimages 1600A to 1600C respectively which are:

-   -   First image 1600A depicts SEM cross-sectional images of the        encapsulated Lame resonator according to an embodiment of the        invention;    -   Second image 1600B depicts packaged resonator dies measuring 1        mm×1 mm; and    -   Third image 1600C depicts a detailed SEM view of the TSV and the        1.5 μm transduction gap.

The resonator die were attached to a circuit board, with epoxy, and wirebonded to the board traces wherein they were characterised with anexperimental configuration as depicted in FIG. 3 wherein the resonatorsare configured with fully differential drive and detection. Differentialdrive being via a power splitter connected to the output of a vectornetwork analyzer with drive power of 0 dBm. For sensing a pair of lowinput bias current transimpedance amplifiers (TIAs) were employed whichwere subsequently combined and amplified using another low noiseinstrumentation amplifier. An example of an extracted frequency responseof a Lame mode resonator according to an embodiment of the invention isdepicted in FIG. 17 . At an applied polarization voltage of 40V, theresonant frequency was 6.8953 MHz, while the quality factor (Q) wascalculated to be 3.24×10⁶ which yields a ƒ−Q product of 22.3×10¹² Hzwhich the inventors believe is the highest reported value forwafer-level vacuum encapsulated silicon resonators.

Now referring to FIG. 18 results for sweeping the polarization voltageare depicted allowing the electrostatic frequency tuning and linearregime of the resonator to be measured. As expected, the resonantfrequency decreases with increasing bias voltage due to electrostaticsoftening effect. The data from the frequency responses was analyzed inorder to extract the motional resistance of the device and derive anexpression for the frequency tuning which are depicted in FIG. 19wherein over the tested range from 10V to 50V there is a linearrelationship between the polarization voltage and the frequency shiftwith an approximate 45 Hz range with a resulting sensitivity of ˜1.1Hz/V The total frequency change is only ˜45 Hz, leading to a sensitivityof approximately 1.1 Hz/V. Beneficially this means frequency stabilityin light of power supply variations as arise in many mobile, portable,and wearable devices. However, temperature tuning is limited. Themotional resistance of the device follows an exponential relation to thebias voltage wherein the lowest value obtained is 37 kΩ at a biasvoltage of 50V. Non-linear effects are introduced above that value.

D. Fabrication

D.1. Exemplary Process Sequence

Referring to FIG. 20A there is depicted an exemplary process flowwherein three sub-process flows for handling wafer, device wafer, andthrough silicon vias (TSVs) are employed. Subsequent to completion ofthe handling wafer processes this is then bonded to the device wafer bywafer-wafer bonding. This assembly then undergoes additional combinedhandling and device wafer processing. In the third process flow TSVs areimplemented as required in the top layer wherein this is then bonded tothe handling/device wafer combination.

FIG. 20B there is depicted an image of a handling wafer lower cavitypattern, e.g. 30 μm recess.

FIG. 20C depicts the handling wafer bonded to the device wafer,typically, 30 μm thick, wherein the device wafer may have beenpre-processed to form other MEMS structures that will be formed as partof the final die. Such MEMS structures, may include, but are not limitedto, temperature sensors, humidity sensors, gas sensors, andaccelerometers, see for example El-Gamal et al in “Methods and Systemsfor Humidity and Pressure Sensor Overlay Integration with Electronics”(U.S. Patent Publication 2014/0,125,359).

FIG. 20D wherein through silicon vias (TSV) are fabricated together withthe upper sense cavity, typically for example 2 μm-5 μm but can bethicker.

FIG. 20E wherein the TSV wafer has the upper cavity formed, typically 30μm deep, followed by formation of the metallization for electricalcontacts. Additionally, the handling/device wafer is bonded to the TSVwafer via wafer-wafer bonding with establishment of the interconnectmetallization.

FIG. 20F depicts an exploded view of final assembled stack for MEMSpressure sensor according to an embodiment of the invention.

The manufacturing sequence described and depicted in FIG. 20A to 20F mayexploit a combination of standard semiconductor processes including, butnot limited to, wet etching, dry etching, photolithography, reactive ionetching, deep reactive ion etching, chemical vapour deposition (CVD),plasma enhanced CVD, electron-beam evaporation, electron beamlithography, and thermal evaporation.

Accordingly, considering such a process flow the resulting structure isa device layer having active elements disposed between upper and lowercavities formed within the top and handling layers respectively. Theenvironment at the time of bonding these top, device and handling layerstogether allows the environment within the cavity or cavities to becontrolled. In the instance the membrane within the device layer is aslarge as the cavity then two cavities are formed but in the instancethat the membrane is not then there is a single cavity with the membrane(i.e. beam) disposed within. Accordingly, a resonator may be packagedwithin a hermetic very low pressure environment for a high qualityfactor or a cavity sealed at very low pressure.

D.2. CMOS Electronics Integration

Referring to FIG. 21 there is depicted an exemplary integrationmethodology for MEMS pressure sensors according to an embodiment of theinvention wherein a fabricated array/die/wafer of MEMS pressure sensors2110 is flipped and aligned relative to a CMOS electronics 2120die/wafer. These are then brought together under conditions that thecontact bumps, e.g. Au/Sn on the CMOS electronics 2120 die/wafer join tothe metallization on the MEMS pressure sensors 2110, e.g. Au/Sn as well,to form a bond and electrical contact.

Beneficially, embodiments of the invention provide a fabrication processwhich is designed to be fully compatible with monolithic integrationabove CMOS electronics, and other electronics technologies that canwithstand the low processing temperatures of embodiments of theinvention. Beneficially this provides:

-   -   direct integration over the electronics;    -   improved system performance through reduced parasitic effects;    -   reduced die size;    -   increased electronics selection freedom, allowing for use of        high performance technological nodes    -   reduced package footprint and thickness;    -   self-aligned processing;    -   lower sensor fabrication costs through batch processing;    -   integral reference elements; and    -   integral heaters and/or temperature stabilization.

The foregoing disclosure of the exemplary embodiments of the presentinvention has been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise forms disclosed. Many variations andmodifications of the embodiments described herein will be apparent toone of ordinary skill in the art in light of the above disclosure. Thescope of the invention is to be defined only by the claims appendedhereto, and by their equivalents.

Further, in describing representative embodiments of the presentinvention, the specification may have presented the method and/orprocess of the present invention as a particular sequence of steps.However, to the extent that the method or process does not rely on theparticular order of steps set forth herein, the method or process shouldnot be limited to the particular sequence of steps described. As one ofordinary skill in the art would appreciate, other sequences of steps maybe possible. Therefore, the particular order of the steps set forth inthe specification should not be construed as limitations on the claims.In addition, the claims directed to the method and/or process of thepresent invention should not be limited to the performance of theirsteps in the order written, and one skilled in the art can readilyappreciate that the sequences may be varied and still remain within thespirit and scope of the present invention.

What is claimed is:
 1. A MEMS device comprising: a MEMS resonatingelement; a movable electrode for electrostatic actuation and sensing ofthe MEMS resonating element, wherein the movable electrode comprises anopening in the movable electrode; a stop anchor located within theopening in the movable electrode; and a welding pad located on (i) asurface of the movable electrode in the opening of the movable electrodeor (ii) a surface of the stop anchor in the opening of the movableelectrode, wherein the movable electrode is configured to move in aparticular direction in response to a voltage applied between themovable electrode and the MEMS resonating element such that, when themovable electrode is moved in the particular direction, the welding padcontacts both the movable electrode and the stop anchor, thereby causingthe surface of the movable electrode to be separated from the surface ofthe stop anchor by a thickness of the welding pad.
 2. The MEMS deviceaccording to claim 1, wherein: the surface of the movable electrode inthe opening of the movable electrode is a first surface; the movableelectrode further comprises a second surface opposite the first surfacein the opening of the movable electrode; the stop anchor is locatedbetween the first and second surfaces of the movable electrode such thatthe stop anchor is separated from the first surface by a first distanceand the stop anchor is separated from the second surface by a seconddistance; the movable electrode further comprises a third surfacenearest the MEMS resonating element; and the third surface of themovable electrode is separated from the MEMS resonating element by athird distance when the movable electrode has not been moved in theparticular direction.
 3. The MEMS device according to claim 2, whereinthe first distance and the third distance are controlled duringfabrication such that, when the movable electrode has not been moved inthe particular direction, the first distance is smaller than the thirddistance.
 4. The MEMS device according to claim 2, wherein, after themovable electrode is moved in the particular direction, the thirdsurface of the movable electrode is separated from the MEMS resonatingelement by a fourth distance that is equivalent to the third distanceminus the first distance plus the thickness of the welding pad.
 5. TheMEMS device according to claim 1, wherein the MEMS resonating elementcomprises a Lame mode resonator.
 6. The MEMS device according to claim1, wherein: the movable electrode is a first movable electrode fromamong a plurality of movable electrodes for electrostatic actuation andsensing of the MEMS resonating element, each respective movableelectrode of the plurality of movable electrodes comprising a respectiveopening in the respective movable electrode, and each respective movableelectrode of the plurality of movable electrodes being configured tomove in the particular direction; the stop anchor is a first stop anchorfrom among a plurality of stop anchors, each respective stop anchor ofthe plurality of stop anchors being located within one of the respectiveopenings in the plurality of movable electrodes; and the welding pad isa first welding pad from among a plurality of welding pads, eachrespective welding pad of the plurality of welding pads being located on(i) a respective surface of one of the respective movable electrodes inone of the respective openings or (ii) a respective surface of one ofthe respective stop anchors in one of the respective openings, suchthat, when the plurality of movable electrodes are moved in theparticular direction, each respective welding pad of the plurality ofwelding pads contacts both one of the respective movable electrodes andone of the respective stop anchors.
 7. A method of post-fabrication gapreduction, the method comprising: fabricating a MEMS device, the MEMSdevice comprising: a MEMS resonating element; a movable electrode forelectrostatic actuation and sensing of the MEMS resonating element,wherein the movable electrode comprises an opening in the movableelectrode; a stop anchor located within the opening in the movableelectrode; and a welding pad located on (i) a surface of the movableelectrode in the opening of the movable electrode or (ii) a surface ofthe stop anchor in the opening of the movable electrode; applying avoltage differential between the movable electrode and the MEMSresonating element, such that the voltage differential causes themovable electrode to move toward the MEMS resonating element until thewelding pad contacts both the movable electrode and the stop anchor; andpassing a current through the welding pad, such that the current issufficiently large to at least partly melt the welding pad and fix themovable electrode in place.
 8. The method according to claim 7, wherein:the surface of the movable electrode in the opening of the movableelectrode is a first surface; the movable electrode further comprises asecond surface opposite the first surface in the opening of the movableelectrode; the stop anchor is located between the first and secondsurfaces of the movable electrode such that the stop anchor is separatedfrom the first surface by a first distance and the stop anchor isseparated from the second surface by a second distance; the movableelectrode further comprises a third surface nearest the MEMS resonatingelement; and the third surface of the movable electrode is separatedfrom the MEMS resonating element by a third distance when the voltagedifferential has not yet been applied.
 9. The method according to claim8, wherein the first distance and the third distance are controlledduring fabrication such that, when the voltage differential has not yetbeen applied, the first distance is smaller than the third distance. 10.The method according to claim 8, wherein, after the voltage differentialcauses the movable electrode to move toward the MEMS resonating element,the third surface of the movable electrode is separated from the MEMSresonating element by a fourth distance that is equivalent to the thirddistance minus the first distance plus the thickness of the welding pad.11. The method according to claim 7, wherein the welding pad issufficiently small such that passing the current through the welding padwill melt at least primarily the welding pad and not the surroundingstructure.
 12. A MEMS device comprising: a MEMS resonating element; amovable electrode for electrostatic actuation and sensing of the MEMSresonating element; a stop anchor, wherein the stop anchor has at leastone surface located between a first surface of the movable electrode andthe MEMS resonating element; and a welding pad located on (i) the firstsurface of the movable electrode, facing the at least one surface of thestop anchor or (ii) the at least one surface of the stop anchor, whereinthe movable electrode is configured to move in a particular direction inresponse to a voltage applied between the movable electrode and the MEMSresonating element such that, when the movable electrode is moved in theparticular direction, the welding pad contacts both the first surface ofthe movable electrode and the at least one surface of the stop anchor,thereby causing the first surface of the movable electrode to beseparated from the at least one surface of the stop anchor by athickness of the welding pad.
 13. The MEMS device according to claim 12,wherein: the at least one surface of the stop anchor is separated fromthe first surface of the movable electrode by a first distance; themovable electrode further comprises a second surface nearest the MEMSresonating element; and the second surface of the movable electrode isseparated from the MEMS resonating element by a second distance when themoveable electrode has not been moved in the particular direction. 14.The MEMS device according to claim 13, wherein the first distance andthe second distance are controlled during fabrication such that, whenthe movable electrode has not been moved in the particular direction,the first distance is smaller than the second distance.
 15. The MEMSdevice according to claim 14, wherein, when the movable electrode ismoved in the particular direction, the second surface of the movableelectrode is separated from the MEMS resonating element by a thirddistance that is equivalent to the second distance minus the firstdistance plus the thickness of the welding pad.
 16. The MEMS deviceaccording to claim 12, wherein: the moveable electrode is a firstmoveable electrode from among a plurality of movable electrodes forelectrostatic actuation and sensing of the MEMS resonating element, eachrespective movable electrode of the plurality of movable electrodescomprising a respective first surface on the respective moveableelectrode, and each respective movable electrode of the plurality ofmovable electrodes being configured to move in the particular direction;the stop anchor is a first stop anchor from among a plurality of stopanchors, each respective stop anchor of the plurality of stop anchorscomprising a respective at least one surface on the respective stopanchor, wherein the respective at least one surface on the respectivestop anchor is located between the MEMS resonating element and one ofthe respective first surfaces in the plurality of moveable electrodes;and the welding pad is a first welding pad from among a plurality ofwelding pads, each respective welding pad of the plurality of weldingpads being located on (i) the respective first surface of one of therespective movable electrodes, facing the respective at least onesurface on the plurality of stop anchors or (ii) the respective at leastone surface of the respective stop anchors, such that, when theplurality of movable electrodes are moved in the particular direction,each respective welding pad of the plurality of welding pads contactsboth one of the respective movable electrodes and one of the respectivestop anchors.